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In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-4 implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for j ≥ 2 (the selection constants are different for j = 0, j = 1, and j ≥ 2), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.